The Dixmier trace and asymptotics of zeta functions

Details The Dixmier trace and asymptotics of zeta functions The Dixmier trace and asymptotics of zeta functions

2006-11-21

arxiv.org/abs/math/0611629v1

Mathematics

Operator Algebras

23 pp, submitted

Scientific paper

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find for p>1 that the asymptotics of the zeta function determines an ideal strictly larger than {\mathcal L}^{p,\infty} on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.

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